Simpson Manufacturing sells a product for $1,600 per unit. Fixed costs are $34,000, while the variable costs are $600 per unit. If the company has a 15% margin of safety, how many units were actually sold?

Question

BlackTom AI · Accepted Answer

We start by outlining the given data and the relationships involved:
- Selling price per unit: $1,600
- Variable cost per unit: $600
- Contribution margin per unit: $1,600 - $600 = $1,000
- Fixed costs: $34,000
- Margin of safety (MOS) required: 15%

Now evaluate each answer option by checking how it fits the margin of safety condition.

Option 1: 25 units
- Total revenue = 25 × $1,600 = $40,000
- Total variable cost = 25 × $600 = $15,000
- Total contribution = 25 × $1,000 = $25,000
- Net profit (before tax) = Contribution − Fixed costs = $25,000 − $34,000 = −$9,000 (a loss)
- Margin of safety would be (Actual units − BEP units) / Actual units, but since this scenario already yields a loss, it does not align with a positive MOS of 15%. In any case, the BEP here would be higher than actual, so MOS cannot be 15%.

Option 2: 50 units
- Total revenue = 50 × $1,600 = $80,000
- Total variable cost = 50 × $600 = $30,000
- Total contribution = 50 × $1,000 = $50,000
- Net profit = $50,000 − $34,000 = $16,000
- BEP units = Fixed costs / Contribution per unit = $34,000 / $1,000 = 34 units
- MOS = (Actual − BEP) / Actual = (50 − 34) / 50 = 16 / 50 = 0.32 = 32%
- This MOS (32%) is higher than the required 15%, so it does not match exactly 15% MOS.

Option 3: 40 units
- Total revenue = 40 × $1,600 = $64,000
- Total variable cost = 40 × $600 = $24,000
- Total contribution = 40 × $1,000 = $40,000
- Net profit = $40,000 − $34,000 = $6,000
- BEP units = 34 (as above)
- MOS = (Actual − BEP) / Actual = (40 − 34) / 40 = 6 / 40 = 0.15 = 15%
- This MOS exactly matches the given 15% requirement, and all calculations are consistent with the data.

Option 4: 34 units
- Total revenue = 34 × $1,600 = $54,400
- Total variable cost = 34 × $600 = $20,400
- Total contribution = 34 × $1,000 = $34,000
- Net profit = $34,000 − $34,000 = $0 (break-even)
- MOS at BEP would be (Actual − BEP) / Actual = (34 − 34) / 34 = 0
- MOS here is 0%, not the 15% required, so this option does not fit the given MOS target.

In summary, evaluating each option against the margin of safety condition shows that only the 40-unit scenario yields exactly a 15% MOS while remaining internally consistent with the fixed and variable costs, and the price per unit. The other options fail to meet the MOS criterion or produce results that are inconsistent with the MOS specification.

Simpson Manufacturing sells a product for $1,600 per unit. Fixed costs are $34,000, while the variable costs are $600 per unit. If the company has a 15% margin of safety, how many units were actually sold?

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